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    "# Bayesian Network Structure Learning in Pomegranate\n",
    "\n",
    "author: Jacob Schreiber <br>\n",
    "contact: jmschreiber91@gmail.com\n",
    "    \n",
    "Learning the structure of Bayesian networks can be complicated for two main reasons: (1) difficulties in inferring causality and (2) the super-exponential number of directed edges that could exist in a dataset. The first issue presents itself when the structure lerning algorithm considers only correlation or another measure of co-occurrence to determine if an edge should exist. The first point presents challenges which deserve a far more in depth treatment unrelated to implementations in pomegranate, so instead this tutorial will focus on how pomegranate implements fast Bayesian network structure learning. It will also cover a new concept called the \"constraint graph\" which can be used to massively speed up structure search while also making causality assignment a bit more reasonable.\n",
    "\n",
    "## Introduction to Bayesian Network Structure Learning\n",
    "\n",
    "Most methods for Bayesian network structure learning (BNSL) can be put into one of the following three categories: \n",
    "\n",
    "(1) Search and Score: The most intuitive method is that of 'search and score,' where one searches over the space of all possible directed acyclic graphs (DAGs) and identifies the one that minimizes some objective function. Typical objective functions attempt to balance the log probability of the data given the model (the likelihood) with the complexity of the model to encourage sparser models. A naive implementation of this search is super-exponential in time with the number of variables, and becomes infeasible when considering even less than a dozen variables. However, dynamic programming can efficiently remove the many repeated calculations and reduce this to be simply exponential in time. This allows exact BNSL to scale to ~25-30 variables. In addition, the A\\* algorithm can be used to smartly search the space and reduce computational time even further by not even considering all possibile networks.\n",
    "\n",
    "(2) Constraint learning: These methods typically involve calculating some measure of correlation or co-occurrence to identify an undirected backbone of edges that could exist, and then prune these edges systematically until a DAG is reached. A common method is to iterate over all triplets of variables to identify conditional independencies that specify both presence and direction of the edges. This algorithm is asymptotically faster (quadratic in time) than search-and-score, but it does not have a simple probabilistic interpretation.\n",
    "\n",
    "(3) Approximate algorithms: In many real world examples, one wishes to merge the interpretability of the search and score method with the attractiveness of the task finishing before the universe ends. To this end, several heuristics have been developed with different properties to yield good structures in a reasonable amount of time. These methods include the Chow-Liu tree building algorithm, the hill-climbing algorithm, and optimal reinsertion, though there are others.\n",
    "\n",
    "pomegranate currently implements a search-and-score method based on the minimum description length score which utilizes the dynamic programming and A\\* algorithm (DP/A\\*), a greedy algorithm based off of DP/A\\*, and the Chow-Liu tree building algorithm, though there are plans to soon add other algorithms.\n",
    "\n",
    "## Structure Learning in pomegranate\n",
    "### Exact Learning\n",
    "\n",
    "Structure learning in pomegranate is done using the `from_samples` method. All you pass in is the samples, their associated weights (if not uniform), and the algorithm which you'd like to use, and it will learn the network for you using the dynamic programming implementation. Lets see a quick synthetic example to make sure that appropriate connections are found. Lets add connections between variables 1, 3, 6, and variables 0 and 2, and variables 4 and 5."
   ]
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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "((), (), (0,), (1,), (), (4,), (3,))\n"
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AWff16ykC27ax04SCwUFupy4qYnItPj407bgODocDJ0+exPPPP4+f/OQneOyxx/Dxxx+H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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f620d0f1f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%pylab inline\n",
    "%load_ext memory_profiler\n",
    "from pomegranate import BayesianNetwork\n",
    "import seaborn, time\n",
    "seaborn.set_style('whitegrid')\n",
    "\n",
    "X = numpy.random.randint(2, size=(2000, 7))\n",
    "X[:,3] = X[:,1]\n",
    "X[:,6] = X[:,1]\n",
    "\n",
    "X[:,0] = X[:,2]\n",
    "\n",
    "X[:,4] = X[:,5]\n",
    "\n",
    "model = BayesianNetwork.from_samples(X, algorithm='exact')\n",
    "print model.structure\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The structure attribute returns a tuple of tuples, where each inner tuple corresponds to that node in the graph (and the column of data learned on). The numbers in that inner tuple correspond to the parents of that node. The results from this structure are that node 3 has node 1 as a parent, that node 2 has node 0 as a parent, and so forth. It seems to faithfully recapture the underlying dependencies in the data.\n",
    "\n",
    "Now, two algorithms for performing search-and-score were mentioned, the traditional shortest path algorithm and the A\\* algorithm. These both work by essentially turning the Bayesian network structure learning problem into a shortest path problem over an 'order graph.' This order graph is a lattice made up of layers of variable sets from the BNSL problem, with the root node having no variables, the leaf node having all variables, and layer `i` in the lattice having all subsets of variables of size `i`. Each path from the root to the leaf represents a certain topological sort of the variables, with the shortest path corresponding to the optimal topological sort and Bayesian network. Details can be found <a href=\"http://url.cs.qc.cuny.edu/publications/Yuan11learning.pdf\">here</a>. The traditional shortest path algorithm calculates the values of all edges in the order lattice before finding the shortest path, while the A\\* algorithm searches only a subset of the order lattice and begins searching immediately. Both methods yield optimal Bayesian networks.\n",
    "\n",
    "A major problem that arises in the traditional shortest path algorithm is that the size of the order graph grows exponentially with the number of variables, and can make tasks infeasible that have otherwise-reasonable computational times. While the A\\* algorithm is faster computationally, another advantage is that it uses a much smaller amount of memory since it doesn't explore the full order graph, and so can be applied to larger problems.\n",
    "\n",
    "In order to see the differences between these algorithms in practice, let's turn to the task of learning a Bayesian network over the digits dataset. The digits dataset is comprised of over a thousand 8x8 pictures of handwritten digits. We binarize the values into 'on' or 'off' for simplicity, and try to learn dependencies between the pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xox/9qCiKovjnP/9ZPP7446XPvHjxYrF69erimWeeKX7/+9+XOutvf/tb8eSTTxZFURQX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\nlRICAABkpYQAAABZ/R8Nfw/WW3uk/gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6204fdc710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "\n",
    "X, y = load_digits(10, True)\n",
    "X = X > numpy.mean(X)\n",
    "\n",
    "plt.figure(figsize=(14, 4))\n",
    "plt.subplot(131)\n",
    "plt.imshow(X[0].reshape(8, 8), interpolation='nearest')\n",
    "plt.grid(False)\n",
    "plt.subplot(132)\n",
    "plt.imshow(X[1].reshape(8, 8), interpolation='nearest')\n",
    "plt.grid(False)\n",
    "plt.subplot(133)\n",
    "plt.imshow(X[2].reshape(8, 8), interpolation='nearest')\n",
    "plt.grid(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shortest Path\n",
      "Time (s):  70.1325659752\n",
      "P(D|M):  -8267.95044748\n",
      "peak memory: 2548.30 MiB, increment: 1805.16 MiB\n",
      "\n",
      "A* Search\n",
      "Time (s):  54.0429809093\n",
      "P(D|M):  -8267.95044748\n",
      "peak memory: 1339.90 MiB, increment: 458.89 MiB\n"
     ]
    }
   ],
   "source": [
    "X = X[:,:18]\n",
    "    \n",
    "tic = time.time()\n",
    "model = BayesianNetwork.from_samples(X, algorithm='exact-dp') # << BNSL done here!\n",
    "t1 = time.time() - tic\n",
    "p1 = model.log_probability(X).sum()\n",
    "\n",
    "tic = time.time()\n",
    "model = BayesianNetwork.from_samples(X, algorithm='exact')\n",
    "t2 = time.time() - tic\n",
    "p2 = model.log_probability(X).sum()\n",
    "\n",
    "\n",
    "print \"Shortest Path\"\n",
    "print \"Time (s): \", t1\n",
    "print \"P(D|M): \", p1\n",
    "%memit BayesianNetwork.from_samples(X, algorithm='exact-dp')\n",
    "print\n",
    "print \"A* Search\"\n",
    "print \"Time (s): \", t2\n",
    "print \"P(D|M): \", p2\n",
    "%memit BayesianNetwork.from_samples(X, algorithm='exact')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These results show that the A\\* algorithm is both computationally faster and requires far less memory than the traditional algorithm, making it a better default for the 'exact' algorithm. The amount of memory used by the BNSL process is under 'increment', not 'peak memory', as 'peak memory' returns the total memory used by everything, while increment shows the difference in peak memory before and after the function has run. \n",
    "\n",
    "### Approximate Learning: Greedy Search (pomegranate default)\n",
    "\n",
    "A natural heuristic when a non-greedy algorithm is too slow is to consider the greedy version. This simple implementation iteratively finds the best variable to add to the growing topological sort, allowing the new variable to draw only from variables already in the topological sort. This is the default in pomegranate because it has a nice balance between producing good (often optimal) graphs and having a small computational cost and memory footprint. However, there is no guarantee that this produces the globally optimal graph.\n",
    "\n",
    "Let's see how it performs on the same dataset as above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Greedy\n",
      "Time (s):  3.88651204109\n",
      "P(D|M):  -8434.74506907\n",
      "peak memory: 850.02 MiB, increment: 3.01 MiB\n"
     ]
    }
   ],
   "source": [
    "tic = time.time()\n",
    "model = BayesianNetwork.from_samples(X) # << Default BNSL setting\n",
    "t = time.time() - tic\n",
    "p = model.log_probability(X).sum()\n",
    "\n",
    "print \"Greedy\"\n",
    "print \"Time (s): \", t\n",
    "print \"P(D|M): \", p\n",
    "%memit BayesianNetwork.from_samples(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approximate Learning: Chow-Liu Trees\n",
    "\n",
    "However, there are even cases where the greedy heuristic is too slow, for example hundreds of variables. One of the first heuristics for BNSL is that of Chow-Liu trees, which learns the optimal tree from data. Essentially it calculates the mutual information between all pairs of variables and then finds the maximum spanning tree. A root node has to be input to turn the undirected edges based on mutual information into directed edges for the Bayesian network. The algorithm is is $O(d^{2})$ and practically is extremely fast and memory efficient, though it produces structures with a worse $P(D|M)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chow-Liu\n",
      "Time (s):  0.0929050445557\n",
      "P(D|M):  -8752.32666094\n",
      "peak memory: 834.77 MiB, increment: 0.00 MiB\n"
     ]
    }
   ],
   "source": [
    "tic = time.time()\n",
    "model = BayesianNetwork.from_samples(X, algorithm='chow-liu') # << Default BNSL setting\n",
    "t = time.time() - tic\n",
    "p = model.log_probability(X).sum()\n",
    "\n",
    "print \"Chow-Liu\"\n",
    "print \"Time (s): \", t\n",
    "print \"P(D|M): \", p\n",
    "%memit BayesianNetwork.from_samples(X, algorithm='chow-liu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison\n",
    "\n",
    "We can then compare the algorithms directly to each other on the digits dataset as we expand the number of pixels to consider."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X, _ = load_digits(10, True)\n",
    "X = X > numpy.mean(X)\n",
    "\n",
    "t1, t2, t3, t4 = [], [], [], []\n",
    "p1, p2, p3, p4 = [], [], [], []\n",
    "n_vars = range(8, 19)\n",
    "\n",
    "for i in n_vars:\n",
    "    X_ = X[:,:i]\n",
    "\n",
    "    tic = time.time()\n",
    "    model = BayesianNetwork.from_samples(X_, algorithm='exact-dp') # << BNSL done here!\n",
    "    t1.append(time.time() - tic)\n",
    "    p1.append(model.log_probability(X_).sum())\n",
    "\n",
    "    tic = time.time()\n",
    "    model = BayesianNetwork.from_samples(X_, algorithm='exact')\n",
    "    t2.append(time.time() - tic)\n",
    "    p2.append(model.log_probability(X_).sum())\n",
    "\n",
    "    tic = time.time()\n",
    "    model = BayesianNetwork.from_samples(X_, algorithm='greedy')\n",
    "    t3.append(time.time() - tic)\n",
    "    p3.append(model.log_probability(X_).sum())\n",
    "\n",
    "    tic = time.time()\n",
    "    model = BayesianNetwork.from_samples(X_, algorithm='chow-liu')\n",
    "    t4.append(time.time() - tic)\n",
    "    p4.append(model.log_probability(X_).sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f620cf27410>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YpUqVbKPm3b17V+17U3p6etn2devWrZeek7m5OVFRUdnesUpISNDI0LRCiKIlMDAQS0vL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\n/fVKM6JdWt8cOHCAr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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f620d098890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 4))\n",
    "plt.subplot(121)\n",
    "plt.title(\"Time to Learn Structure\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.ylabel(\"Time (s)\", fontsize=14)\n",
    "plt.xlabel(\"Variables\", fontsize=14)\n",
    "plt.plot(n_vars, t1, c='c', label=\"Exact Shortest\")\n",
    "plt.plot(n_vars, t2, c='m', label=\"Exact A*\")\n",
    "plt.plot(n_vars, t3, c='g', label=\"Greedy\")\n",
    "plt.plot(n_vars, t4, c='r', label=\"Chow-Liu\")\n",
    "plt.legend(fontsize=14, loc=2)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.title(\"$P(D|M)$ with Resulting Model\", fontsize=14)\n",
    "plt.xlabel(\"Variables\", fontsize=14)\n",
    "plt.ylabel(\"logp\", fontsize=14)\n",
    "plt.plot(n_vars, p1, c='c', label=\"Exact Shortest\")\n",
    "plt.plot(n_vars, p2, c='m', label=\"Exact A*\")\n",
    "plt.plot(n_vars, p3, c='g', label=\"Greedy\")\n",
    "plt.plot(n_vars, p4, c='r', label=\"Chow-Liu\")\n",
    "plt.legend(fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the expected results-- that the A\\* algorithm works faster than the shortest path, the greedy one faster than that, and Chow-Liu the fastest. The purple and cyan lines superimpose on the right plot as they produce graphs with the same score, followed closely by the greedy algorithm and then Chow-Liu performing the worst."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraint Graphs\n",
    "\n",
    "Now, sometimes you have prior information about how groups of nodes are connected to each other and want to exploit that. This can take the form of a global ordering, where variables can be ordered in such a manner that edges only go from left to right, for example. However, sometimes you have layers in your network where variables are a part of these layers and can only have parents in another layer.\n",
    "\n",
    "Lets consider a diagnostics Bayesian network like the following (no need to read code, the picture is all that is important for now):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/Nzc3h5s3b+LMmTNobm5esQ5MTk6iqakJPT090Gq12Lp1KxITEyGXy59qyKpU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\nHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61e3b2a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pomegranate import DiscreteDistribution, ConditionalProbabilityTable, Node\n",
    "\n",
    "BRCA1 = DiscreteDistribution({0: 0.999, 1: 0.001})\n",
    "BRCA2 = DiscreteDistribution({0: 0.985, 1: 0.015})\n",
    "LCT   = DiscreteDistribution({0: 0.950, 1: 0.050})\n",
    "\n",
    "OC = ConditionalProbabilityTable([[0, 0, 0, 0.999],\n",
    "                                  [0, 0, 1, 0.001],\n",
    "                                  [0, 1, 0, 0.750],\n",
    "                                  [0, 1, 1, 0.250],\n",
    "                                  [1, 0, 0, 0.700],\n",
    "                                  [1, 0, 1, 0.300],\n",
    "                                  [1, 1, 0, 0.050],\n",
    "                                  [1, 1, 1, 0.950]], [BRCA1, BRCA2])\n",
    "\n",
    "LI = ConditionalProbabilityTable([[0, 0, 0.99],\n",
    "                                  [0, 1, 0.01],\n",
    "                                  [1, 0, 0.20],\n",
    "                                  [1, 1, 0.80]], [LCT])\n",
    "\n",
    "PREG = DiscreteDistribution({0: 0.90, 1: 0.10})\n",
    "\n",
    "LE = ConditionalProbabilityTable([[0, 0, 0.99],\n",
    "                                  [0, 1, 0.01],\n",
    "                                  [1, 0, 0.25],\n",
    "                                  [1, 1, 0.75]], [OC])\n",
    "\n",
    "BLOAT = ConditionalProbabilityTable([[0, 0, 0, 0.85],\n",
    "                                     [0, 0, 1, 0.15],\n",
    "                                     [0, 1, 0, 0.70],\n",
    "                                     [0, 1, 1, 0.30],\n",
    "                                     [1, 0, 0, 0.40],\n",
    "                                     [1, 0, 1, 0.60],\n",
    "                                     [1, 1, 0, 0.10],\n",
    "                                     [1, 1, 1, 0.90]], [OC, LI])\n",
    "\n",
    "LOA = ConditionalProbabilityTable([[0, 0, 0, 0.99],\n",
    "                                   [0, 0, 1, 0.01],\n",
    "                                   [0, 1, 0, 0.30],\n",
    "                                   [0, 1, 1, 0.70],\n",
    "                                   [1, 0, 0, 0.95],\n",
    "                                   [1, 0, 1, 0.05],\n",
    "                                   [1, 1, 0, 0.95],\n",
    "                                   [1, 1, 1, 0.05]], [PREG, OC])\n",
    "\n",
    "VOM = ConditionalProbabilityTable([[0, 0, 0, 0, 0.99],\n",
    "                                   [0, 0, 0, 1, 0.01],\n",
    "                                   [0, 0, 1, 0, 0.80],\n",
    "                                   [0, 0, 1, 1, 0.20],\n",
    "                                   [0, 1, 0, 0, 0.40],\n",
    "                                   [0, 1, 0, 1, 0.60],\n",
    "                                   [0, 1, 1, 0, 0.30],\n",
    "                                   [0, 1, 1, 1, 0.70],\n",
    "                                   [1, 0, 0, 0, 0.30],\n",
    "                                   [1, 0, 0, 1, 0.70],\n",
    "                                   [1, 0, 1, 0, 0.20],\n",
    "                                   [1, 0, 1, 1, 0.80],\n",
    "                                   [1, 1, 0, 0, 0.05],\n",
    "                                   [1, 1, 0, 1, 0.95],\n",
    "                                   [1, 1, 1, 0, 0.01],\n",
    "                                   [1, 1, 1, 1, 0.99]], [PREG, OC, LI])\n",
    "\n",
    "AC = ConditionalProbabilityTable([[0, 0, 0, 0.95],\n",
    "                                  [0, 0, 1, 0.05],\n",
    "                                  [0, 1, 0, 0.01],\n",
    "                                  [0, 1, 1, 0.99],\n",
    "                                  [1, 0, 0, 0.40],\n",
    "                                  [1, 0, 1, 0.60],\n",
    "                                  [1, 1, 0, 0.20],\n",
    "                                  [1, 1, 1, 0.80]], [PREG, LI])\n",
    "\n",
    "s1 = Node(BRCA1, name=\"BRCA1\")\n",
    "s2 = Node(BRCA2, name=\"BRCA2\")\n",
    "s3 = Node(LCT, name=\"LCT\")\n",
    "s4 = Node(OC, name=\"OC\")\n",
    "s5 = Node(LI, name=\"LI\")\n",
    "s6 = Node(PREG, name=\"PREG\")\n",
    "s7 = Node(LE, name=\"LE\")\n",
    "s8 = Node(BLOAT, name=\"BLOAT\")\n",
    "s9 = Node(LOA, name=\"LOA\")\n",
    "s10 = Node(VOM, name=\"VOM\")\n",
    "s11 = Node(AC, name=\"AC\")\n",
    "\n",
    "model = BayesianNetwork(\"Hut\")\n",
    "model.add_nodes(s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11)\n",
    "model.add_edge(s1, s4)\n",
    "model.add_edge(s2, s4)\n",
    "model.add_edge(s3, s5)\n",
    "model.add_edge(s4, s7)\n",
    "model.add_edge(s4, s8)\n",
    "model.add_edge(s4, s9)\n",
    "model.add_edge(s4, s10)\n",
    "model.add_edge(s5, s8)\n",
    "model.add_edge(s5, s10)\n",
    "model.add_edge(s5, s11)\n",
    "model.add_edge(s6, s9)\n",
    "model.add_edge(s6, s10)\n",
    "model.add_edge(s6, s11)\n",
    "model.bake()\n",
    "\n",
    "plt.figure(figsize=(14, 10))\n",
    "model.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This network contains three layer, with symptoms on the bottom (low energy, bloating, loss of appetite, vomitting, and abdominal cramps), diseases in the middle (overian cancer, lactose intolerance, and pregnancy), and genetic tests on the top for three different genetic mutations. The edges in this graph are constrainted such that symptoms are explained by diseases, and diseases can be partially explained by genetic mutations. There are no edges from diseases to genetic conditions, and no edges from genetic conditions to symptoms. If we were going to design a more efficient search algorithm, we would want to exploit this fact to drastically reduce the search space of graphs.\n",
    "\n",
    "Before presenting a solution, lets also consider another situation. In some cases you can define a global ordering of the variables, meaning you can order them from left to right and ensure that edges only go from the left to the right. This can represent some temporal separation (things on the left happen before things on the right), physical separation, or anything else. This would also dramatically reduce the search space. \n",
    "\n",
    "In addition to reducing the search space, an efficient algorithm can exploit this layered structure. A key property of most scoring functions is the idea of \"global parameter independence\", meaning that that the parents of node A are independent of the parents of node B assuming that they do not form a cycle in the graph. If you have a layered structure, either like in the diagnostics network or through a global ordering, it is impossible to form a cycle in the graph through any valid assignment of parent values. This means that the parents for each node can be identified independently, drastically reducing the runtime of the algorithm.\n",
    "\n",
    "Now, sometimes we know ~some things~ about the structure of the variables, but nothing about the others. For example, we might have a partial ordering on some variables but not know anything about the others. We could enforce an arbitrary ordering on the others, but this may not be well justified. In essence, we'd like to exploit whatever information we have.\n",
    "\n",
    "Abstractly, we can think about this in terms of constraint graphs. Lets say you have some symptoms, diseases, and genetic tests, and don't a priori know the connection between all of these pieces, but you do know the previous layer structure. You can define a \"constraint graph\" which is made up of three nodes, \"symptoms\", \"diseases\", and \"genetic mutations\". There is a directed edge from genetic mutations to diseases, and a directed edge from diseases to symptoms. This specifies that genetic mutations can be parents to diseases, and diseases to symptoms. It would look like the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2bNmCnJyc4G9ZLBbIZDJkZmYiOzs7mF5QX18Pn8+HlJQU5OXlISMjA9nZ2Sgp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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6252b848d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx\n",
    "from pomegranate.utils import plot_networkx\n",
    "\n",
    "constraints = networkx.DiGraph()\n",
    "constraints.add_edge('genetic conditions', 'diseases')\n",
    "constraints.add_edge('diseases', 'symptoms')\n",
    "plot_networkx(constraints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All variables corresponding to these categories would be put in their appropriate name. This would define a scaffold for structure learning.\n",
    "\n",
    "Now, we can do the same thing for a global ordering. Lets say we have 3 variables in an order from 0-2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XtG0b8LWvUTImmeLW8SQzE9iwgVySvj7yxc+dozqbCEmmBaX81TEwQIulpiZK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61e3257410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "constraints = networkx.DiGraph()\n",
    "constraints.add_edge(0, 1)\n",
    "constraints.add_edge(1, 2)\n",
    "constraints.add_edge(0, 2)\n",
    "plot_networkx(constraints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this graph, we're saying that variable 0 can be a parent for 1 or 2, and that variable 1 can be a parent for variable 2. In the same way that putting multiple variables in a node of the constraint graph allowed us to define layers, putting a single variable in the nodes of a constraint graph can allow us to define an ordering.\n",
    "\n",
    "To be specific, lets say we want to find the parents of the variables in node 1 given that those variables parents can only come from the variables in node 0. We can independently find the best parents for each variable in node 1 from the set of those in node 0. This is significantly faster than trying to find the best Bayesian network of all variables in nodes 0 and 1. We can also do the same thing for the variables in node 2 by going through the variables in both nodes 0 and 1 to find the best parent set for the variables in node 2.\n",
    "\n",
    "However, there are some cases where we know nothing about the parent structure of some variables. This can be solved by including self-loops in the graph, where a node is its own parent. This means that we know nothing about the parent structure of the variables in that node and that the full exponential time algorithm will have to be run. The naive structure learning algorithm can be thought of as putting all variables in a single node in the constraint graph and putting a self-loop on that node. \n",
    "\n",
    "We are thus left with two procedures; one for solving edges which are self edges, and one for solving edges which are not. Even though we have to use the exponential time procedure on variables in nodes with self loops, it will still be significantly faster because we will be using less variables (except in the naive case).\n",
    "\n",
    "Frequently though we will have some information about some of the nodes of the graph even if we don't have information about all of the nodes. Lets take the case where we know some variables have no children but can have parents, and know nothing about the other variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hwPnz5/Hll19iZGTkvbTmHjyhC+x2ij2ZpPueSADffqsstc3MMF5XWz/zYaZe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f620c6b0650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "constraints = networkx.DiGraph()\n",
    "constraints.add_edge(0, 1)\n",
    "constraints.add_edge(0, 0)\n",
    "plot_networkx(constraints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this situation we would have to run the exponential time algorithm on the variables in node 0 to find the optimal parents, and then run the independent parents algorithm on the variables in node 1 drawing only from the variables in node 0. To be specific:\n",
    "\n",
    "(1) Use exponential time procedure to find optimal structure amongst variables in node 0 \n",
    "(2) Use independent-parents procedure to find the best parents of variables in node 1, restricting the parents to be in node 0\n",
    "(3) Concatenate these parent sets together to get the optimal structure of the network given the constraints.\n",
    "\n",
    "We can generalize this to any arbitrary constraint graph:\n",
    "\n",
    "(1) Use exponential time procedure to find optimal structure amongst variables in nodes with self loops (including parents from other nodes if needed)\n",
    "(2) Use independent-parents procedure to find best parents of variables in a node given the constraint that the parents must come from variables in the node which is this nodes parent\n",
    "(3) Concatenate these parent sets together to get the optimal structure of the network given the constraints.\n",
    "\n",
    "According to the global parameter independence property of Bayesian networks, this procedure will give the globally optimal Bayesian network while exploring a significantly smaller part of the network.\n",
    "\n",
    "pomegranate supports constraint graphs in an extremely easy to use manner. Lets say that we have a graph with three layers like the diagnostic model, and five variables in each layer. We can define the constraint graph as a networkx DiGraph, with the nodes being tuples containing the column ids of each variable belonging to that variable.\n",
    "\n",
    "In this case, we're saying that (0, 1, 2, 3, 4) is the first node, (5, 6, 7, 8, 9) is the second node, and (10, 11, 12, 13, 14) is the final node. Lets make nodes 1, 7, and 12 related, 11, 13, 14 related, and 3 and 5 related. In this case, where should be an edge from 1 to 7, and 7 to 12. 11, 13, and 14 are all a part of the same layer and so that connection should be ignored, and then there should be a connection from 3 to 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constraint Graph\n"
     ]
    },
    {
     "data": {
      "image/png": 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Iw4QAjtyHkbsEIAJ6go/sjzYKIYaRCHlXXu9nvSufL24eD4WMQ0NxgRIml5NY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\nDVzQOBxO1PD/ljCWItg7UIUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61e3816990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned Bayesian Network\n"
     ]
    },
    {
     "data": {
      "image/png": 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YYWTjlMH69alsG8WMGVREDQ79djgcCAsLQ3BwcLHzJyQkBCEhIeaduxwOGv53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\nTifnMa0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6204d99f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pomegranate time:  0.339829921722 ((), (), (), (), (), (3,), (), (1,), (), (), (), (), (7,), (), ())\n"
     ]
    }
   ],
   "source": [
    "numpy.random.seed(6)\n",
    "\n",
    "X = numpy.random.randint(2, size=(200, 15))\n",
    "\n",
    "X[:,1] = X[:,7]\n",
    "X[:,12] = 1 - X[:,7]\n",
    "\n",
    "X[:,5] = X[:,3]\n",
    "\n",
    "X[:,13] = X[:,11]\n",
    "X[:,14] = X[:,11]\n",
    "\n",
    "a = networkx.DiGraph()\n",
    "b = tuple((0, 1, 2, 3, 4))\n",
    "c = tuple((5, 6, 7, 8, 9))\n",
    "d = tuple((10, 11, 12, 13, 14))\n",
    "\n",
    "a.add_edge(b, c)\n",
    "a.add_edge(c, d)\n",
    "print \"Constraint Graph\"\n",
    "plot_networkx(a)\n",
    "plt.show()\n",
    "\n",
    "print \"Learned Bayesian Network\"\n",
    "\n",
    "tic = time.time()\n",
    "model = BayesianNetwork.from_samples(X, algorithm='exact', constraint_graph=a)\n",
    "\n",
    "plt.figure(figsize=(16, 8))\n",
    "model.plot()\n",
    "plt.show()\n",
    "print \"pomegranate time: \", time.time() - tic, model.structure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that reconstructed perfectly here. Lets see what would happen if we didn't use the exact algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uJVi7lgeYa3VWY1MTk4O77tJ3wxMAdXV1eO2117Bo0SIcOXIESUlJ+L//+z9c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\nZmiacp08aecIJyW5fuYqAABRJZCpn3hCqq62wjSI+SM+Pl5FRUW6444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khgapsVFqamr/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\nAAAAALju/wNrG1zJgJYm9QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6197425350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pomegranate time:  3.44430494308 ((), (), (), (), (), (3,), (), (1,), (), (), (), (), (7,), (11,), (13,))\n"
     ]
    }
   ],
   "source": [
    "tic = time.time()\n",
    "model = BayesianNetwork.from_samples(X, algorithm='exact')\n",
    "plt.figure(figsize=(16, 8))\n",
    "model.plot()\n",
    "plt.show()\n",
    "print \"pomegranate time: \", time.time() - tic, model.structure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like we got three desirable attributes by using a constraint graph. The first is that there was over an order of magnitude speed improvement in finding the optimal graph. The second is that we were able to remove some edges we didn't want in the final Bayesian network, such as those between 11, 13, and 14. We also removed the edge between 1 and 12 and 1 and 3, which are spurious given the model that we originally defined. The third desired attribute is that we can specify the direction of some of the edges and get a better causal model.\n",
    "\n",
    "Lets take a look at how big of a model we can learn given a three layer constraint graph like before. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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e+nclClc3OLPZzKhRo/j5558ZO3YsHTp0AGDnzp0sWLCAL774gg8++AAvL69y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\nAAABQLgCAAAAgAD4//mNe2jdHih+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f620cfdeb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "constraint_times, times = [], []\n",
    "\n",
    "x = numpy.arange(1, 7)\n",
    "for i in x:\n",
    "    symptoms = tuple(range(i))\n",
    "    diseases = tuple(range(i, i*2))\n",
    "    genetic = tuple(range(i*2, i*3))\n",
    "\n",
    "    constraints = networkx.DiGraph()\n",
    "    constraints.add_edge(genetic, diseases)\n",
    "    constraints.add_edge(diseases, symptoms)\n",
    "    \n",
    "    X = numpy.random.randint(2, size=(2000, i*3))\n",
    "    \n",
    "    tic = time.time()\n",
    "    model = BayesianNetwork.from_samples(X, algorithm='exact', constraint_graph=constraints)\n",
    "    constraint_times.append( time.time() - tic )\n",
    "    \n",
    "    tic = time.time()\n",
    "    model = BayesianNetwork.from_samples(X, algorithm='exact')\n",
    "    times.append( time.time() - tic )  \n",
    "\n",
    "\n",
    "plt.figure(figsize=(14, 6))\n",
    "plt.title('Time To Learn Bayesian Network', fontsize=18)\n",
    "plt.xlabel(\"Number of Variables\", fontsize=14)\n",
    "plt.ylabel(\"Time (s)\", fontsize=14)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.plot( x*3, times, linewidth=3, color='c', label='Exact')\n",
    "plt.plot( x*3, constraint_times, linewidth=3, color='m', label='Constrained')\n",
    "plt.legend(loc=2, fontsize=16)\n",
    "plt.yscale('log')"
   ]
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    "Looks like by including a constraint graph, we can far more quickly find the optimal Bayesian network. This can allow us to create Bayesian networks on dozens of variables as long as we can order them into layers.\n",
    "\n",
    "## Other Parameters\n",
    "\n",
    "There are three other parameters that are worth mentioning. The first is that a vector of weights can be passed in alongside a matrix of samples, with each entry in the vector corresponding to the weight of that sample. By default all weights are set to 1, but they can be any non-negative number.\n",
    "\n",
    "```\n",
    "model = BayesianNetwork.from_samples(X, weights=weights)\n",
    "```\n",
    "\n",
    "Next is the pseudocounts parameter that indicates the number added to the observations of each observed variable combination. This acts as a regularizer by smoothing over the counts and is typically used to prevent the model from saying it is impossible for a combination of variables to occur together just because they weren't observed in the data. Currently all learning algorithms support pseudocounts. By default this is set to 0.\n",
    "\n",
    "```\n",
    "model = BayesianNetwork.from_samples(X, pseudocount=1.7\n",
    "```\n",
    "\n",
    "Lastly, the maximum number of parents that each variable can have can be limited. This is sometimes referred to as the k-learn problem in literature. In practice this can dramatically speed up the BNSL task as the majority of time is spent determining the best parent sets. Currently this only affects the exact and greedy algorithm as in the Chow-Liu algorithm each variable only has a single parent.\n",
    "\n",
    "```\n",
    "model = BayesianNetwork.from_samples(X, algorithm='exact', max_parents=2)\n",
    "```\n",
    "\n",
    "Since exact inference uses minimum description length as a score function, the maximum number of parents is by default set to $\\log \\left(\\frac{n}{\\log(n)} \\right)$ with $n$ being the number of samples in the dataset.\n",
    "\n",
    "# Conclusions\n",
    "\n",
    "pomegranate currently supports exact BNSL through an a shortest path dynamic programming algorithm, an A\\* algorithm, a greedy algorithm, the Chow-Liu tree building algorithm, and a constraint-graph based algorithm which can significantly speed up structure learning if you have any prior knowledge of the interactions between variables.\n",
    "\n",
    "If you have any suggestions for how to improve pomegranate or ideas for algorithms to implement, feel free to open an issue on the issue tracker! I'd love to hear feedback."
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